Circular number puzzle
SH...@slacvm.slac.stanford.edu
ABCDEF * 2 = CDEFAB
ABCDEF * 3 = BCDEFA
ABCDEF * 4 = EFABCD
ABCDEF * 5 = FABCDE
ABCDEF * 6 = DEFABC
Every "A" is the same number, as is every other letter.
No two letters are the same number. No zeros.
It is possible. Good luck.
Rich Wenner
Not only possible, but piece of cake! But just in case, here's a
SPOILER ALERT !!!
ABCDEF = 142857, which is the digit pattern that repeats in the fraction
1/7.
For grins, note that Shere had to quit giving clues after
ABCDEF * 6 = DEFABC, because
ABCDEF * 7 = 999999
--
Rich Wenner --(o)--(o)-- I really hate this damn machine.
EDS/TSD/DSD/FSD/CSDPS ( /\ ) I wish that they would sell it.
mmmm It never does quite what I mean,
#include <stddisclaimer.h> \____/ But only what I tell it.
MYU...@slacvm.slac.stanford.edu
Organization: Stanford Linear Accelerator Center
Date: Monday, 30 Mar 1992 13:24:33 PST
From: <SH...@SLACVM.SLAC.STANFORD.EDU>
Message-ID: <92090.13...@SLACVM.SLAC.STANFORD.EDU>
Newsgroups: rec.puzzles
Subject: Circular number puzzle
> "Circular" number puzzle for you all.....
>
> ABCDEF * 2 = CDEFAB
> ABCDEF * 3 = BCDEFA
> ABCDEF * 4 = EFABCD
> ABCDEF * 5 = FABCDE
> ABCDEF * 6 = DEFABC
Spoiler:
ABCDEF=142857
Hong Liang Xie
>
> ABCDEF * 2 = CDEFAB
> ABCDEF * 3 = BCDEFA
> ABCDEF * 4 = EFABCD
> ABCDEF * 5 = FABCDE
> ABCDEF * 6 = DEFABC
>
(SPOILER)
EASY.
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142
Just observe that A = 1 from the last equation.
Then F = 7 by the second equation, as 7 * 3 = 1 (mod 100).
Now it follows that B = 4, D = 8, E = 5, C = 2.
------------------
-Hong, CIS Dept, U of Penn
Ethan Rutter
A B C D E F
1 4 2 8 5 7
Ethan.
--
-------------------------------------------------------------------------
Ethan Rutter | "If I claim to be a wise man,
earu...@athena.cas.vanderbilt.edu | it surely means that I don't know."
Math Dept. | - Carry On Wayward Son, by Kansas
Tom Carmichael
Answer follows...
The number is 142857
(A=1
B=4
C=2
D=8
E=5
F=7)
Tom
--
"Sleep is a poor substitute for caffine."| Tom Carmichael
- The Wizardry Compiled | tac...@hertz.njit.edu
-----------------------------------------| to...@shock.njit.edu
#include <stddisclamer.h> |
Mick Gulovsen
At last an easy one
S> ABCDEF * 2 = CDEFAB
S> ABCDEF * 3 = BCDEFA
S> ABCDEF * 4 = EFABCD
S> ABCDEF * 5 = FABCDE
S> ABCDEF * 6 = DEFABC
By reasoning A MUST be 1 to keep the result of the x 6 calc to a 6 digit No.
After that it is a simple matter to get the rest (ie x3 ends with a 1 MUST mean
F=7 etc).
Here is the result
A=1
B=4
C=2
D=8
E=5
F=7
CYA
* Origin: Andy's BBS: Melb Australia - 61-3-359-6378 (3:635/503)
Raghunath K Rao
Generates the 6 digit repeating sequence of 1/7 = 0.142857142857.
---------------------------------------------------------------------
_____ ___ _______
K. RAGHUNATH RAO /____/ \ /__/\ /______/\
email : ths...@iitmax.iit.edu | __ \ /| / _ \ \ / ___ \ |
sleepy (res) : (312)791-9428 | |__) |/ / /_\ \ \ | / | \ | |
sleepier (off) : (312)567-3407 | __ /\ | ___ | | | | | | | |
| | \ \ \ | / | \ | | | | |_| | |
It is the intonation and not | | |\ \ \ | | | | | | | \/__/ |/
the intention that matters!! |_|/ \_\/ |_|/ |_|/ \______/
---------------------------------------------------------------------
Thorne Kontos
Once you determine A=1, the rest of the digits fall into place
quickly...
Therefore:
The solution is:
A=1, B=4, C=2, D=8, E=5, F=7
Shankar Hemmady
It is also interesting to observe that the number 142857 is the recurring
sequence that you obtain for 1/7
1/7 = 0.142857 142857 ...
Now 2/7, 3/7, 4/7, 5/7, 6/7 correspond to the recurring circular sequences which
are the same numbers in the problem.
-Shankar Hemmady
Rich Wenner
>>
>> ABCDEF * 2 = CDEFAB
Etc. (you've seen it a bazillion times by now).
>Generates the 6 digit repeating sequence of 1/7 = 0.142857142857.
Yes, this is true, and before someone else starts an eternal
thread, let me say that yes, a variation of the same trick works
with the reciprocals of 19, 29, 97, and many other numbers. I can
not find any number N whose reciprocal is a repeating decimal of N-1
digits for which the trick does not work. If someone has a proof
or disproof, I'd like to see it via email, but let's not bore
everybody else with it, OK? If you have a proof, you and I are probably
the only ones in the universe who care. ;-)
>
>---------------------------------------------------------------------
> _____ ___ _______
>K. RAGHUNATH RAO /____/ \ /__/\ /______/\
>email : ths...@iitmax.iit.edu | __ \ /| / _ \ \ / ___ \ |
>sleepy (res) : (312)791-9428 | |__) |/ / /_\ \ \ | / | \ | |
>sleepier (off) : (312)567-3407 | __ /\ | ___ | | | | | | | |
> | | \ \ \ | / | \ | | | | |_| | |
>It is the intonation and not | | |\ \ \ | | | | | | | \/__/ |/
>the intention that matters!! |_|/ \_\/ |_|/ |_|/ \______/
>
>---------------------------------------------------------------------
--
Rich Wenner --(o)--(o)-- I really hate this damn machine.
EDS/TSD/DSD/FSD/CSDPS ( /\ ) I wish that they would sell it.
\ mmmm / It never does quite what I mean,